There is generally a limit to linearity of output signals of a power amplifier for radio, transmission, and particularly a gain decreases when the level of an input signal is large (linearity distortion). As a circuit for compensating for such a linearity distortion, a Cartesian feedback distortion compensating device is known. If a Cartesian feedback distortion compensating device ideally functions, high linearity of output signals of a power amplifier is obtained.
In a Cartesian feedback distortion compensating device, output signals of a power amplifier are taken out and are fed back to the input side. At this point, a phase shift in a feedback system occurs by the influence of, for example, antenna loads, a propagation delay between a directional coupler and a demodulator, or the like. Therefore, in order for a Cartesian feedback distortion compensating device to effectively operate, a phase shift in the feedback system needs to be corrected.
From such a viewpoint, a phase corrector to be applied to a Cartesian feedback distortion compensating device is known. FIG. 1 illustrates the main parts of the phase corrector.
With reference to FIG. 1, an in-phase component I and a quadrature component Q of a transmission base band signal are modulated by a quadrature modulator 40 and then are combined with each other. The resultant composite signal is amplified to a desired level by a power amplifier (PA) 90 and is transmitted as an RF signal (RF_OUT). Part of the RF signal (RF_OUT) is taken out (fed back) by a directional coupler. From the fed back signal y(t), a base band signal (in-phase component I*, quadrature component Q*) is generated by a quadrature demodulator 30. Here, I≠I* and Q≠Q* result from the above-described phase shift (in FIG. 1, a delay corresponding to the phase shift is denoted as a delay time “τ”) of the feedback system, and therefore a phase corrector for correcting the phase shift is provided.
With reference to FIG. 1, a phase corrector includes a phase detector having a sine detecting unit 101 and a cosine detecting unit 102, and a phase shifter 104. Given that a target phase correction amount (i.e., phase error) is Δφ, the fed back base band signal (in-phase component I*, quadrature component Q*) is expressed as the following equations (1) and (2). In equations (1) and (2), I=I* and Q=Q* hold merely for Δφ=0. Sin (Δφ) is calculated in the sine detecting unit 101, according to the following equation (3), where k is a normalization constant and k=1/(I·I+Q·Q).I*=I·cos(Δφ)+Q·sin(−Δφ)  (1)Q*=I·sin(Δφ)+Q·cos(Δφ)  (2)sin(Δφ)=k·(I·Q*−Q·I*)  (3)
The cosine detecting unit 102 calculates cos (Δφ) in accordance with the relationship: cos(Δφ)=(1−sin2(Δφ))1/2. The cosine detecting unit 102 is configured such that the sum of squares of an input to the phase shifter 104 is a given constant Mag. This compensates for the error so as to keep constant the amplitude of an output signal of the phase shifter 104.
In the phase shifter 104, a carrier signal Sin(ωt) from a local oscillator and a signal obtained by shifting the phase of the carrier signal by π/2 are multiplied by sin(Δφ) and cos(Δφ), respectively, and they are combined, as represented by the following equation (4). As a result, a signal sin(ωt+Δφ) whose phase leads the phase of the carrier signal sin(ωt) from the local oscillator just by Δφ is supplied to the quadrature modulator 40. Therefore, the phase error between the RF signal y(t) fed back from the output of the radio transmitter and the carrier signal provided to the quadrature modulator 40 becomes 0 (Δφ=0).cos(Δφ)·sin(ω·t)+sin(Δφ)·cos(ω·t)=sin(ωt+Δφ)  (4)
In a Cartesian feedback distortion compensating device illustrated in FIG. 1, the stability of the feedback control system depends on a loop transfer function. Here, the loop transfer function of the system varies according to the phase error Δφ. Therefore, the stability of the system may be damaged depending on the value of the phase error Δφ. At worst, the damaged stability will cause a transmission base band signal to oscillate.
Further description of the above issue is given as follows.
Given that an input (input base band signal) to the system is X(s), and the loop transfer function of the Cartesian feedback system is L(s, Δφ), an error signal e(s) due to feedback (an error between a negative input base band signal and a fed back base band signal) is expressed by the following equation (5), where s is a Laplace operator.
                              e          ⁡                      (            s            )                          =                              X            ⁡                          (              s              )                                            1            +                          L              ⁡                              (                                  s                  ,                  Δϕ                                )                                                                        (        5        )            
As is apparent from equation (5), this system becomes unstable as the loop transfer function L(s, Δφ) approaches −1. In other words, even when the system is designed as an ideal feedback system with no phase error Δφ, a phase error Δφ actually exists. In the case where the phase error Δφ is very large at an early stage of the system at which phase correction has not yet been performed, and the like, the system sometimes becomes unstable. If the system becomes unstable, an error signal due to feedback will oscillate at worst as mentioned above. Once the oscillation of the error signal occurs, it becomes difficult for the feedback system to function properly.